Hmm. Well, the brief answer is: no, this doesn't happen to bike parts.
Keep in mind, tension on a bike cable or chain is super low when the
bike is sitting still. And neither one comes anywhere near yield point
stress in normal operation. Even if the metal were to magically shorten
a bit, tension would barely change, because of the spring in the brake
or derailleur mechanism.
But honestly, I'm not aware of it happening to guitar strings either.
I'm a near-ex guitarist, which means I still play some, but I've mostly
switched to other instruments. The result is the strings on guitars and
mandolins get changed only very rarely, less than once per year.
(Sacrilege, I know.) I've never seen evidence that letting these
strings sit increases their tension.
The evidence would be this: If corrosion caused increased tension, the
strings would be above concert pitch when I finally took the instrument
out of the case. I haven't seen that. And in general, I think changes
in pitch are much more likely from changes in humidity affecting the
wood, than from any change in the metal itself.
Finally, I don't think the strings are normally at yield stress. I
haven't checked their numbers, but see the graph at the bottom of
http://www.noyceguitars.com/technotes/articles/t3.html
--
- Frank Krygowski